Angiography by Optical Coherence Tomography is a non-invasive retinal imaging modality of recent appearance that allows the visualization of the vascular structure at predefined depths based on the detection of the blood movement. OCT-A images constitute a suitable scenario to analyse the retinal vascular properties of regions of interest, measuring the characteristics of the foveal vascular and avascular zones. Extracted parameters of this region can be used as prognostic factors that determine if the patient suffers from certain pathologies, indicating the associated pathological degree. The manual extraction of these biomedical parameters is a long, tedious and subjective process, introducing a significant intra and inter-expert variability, which penalizes the utility of the measurements. In addition, the absence of tools that automatically facilitate these calculations encourages the creation of computer-aided diagnosis frameworks that ease the doctor's work, increasing their productivity and making viable the use of this type of vascular biomarkers. We propose a fully automatic system that identifies and precisely segments the region of the foveal avascular zone (FAZ) using a novel ophthalmological image modality as is OCT-A. The system combines different image processing techniques to firstly identify the region where the FAZ is contained and, secondly, proceed with the extraction of its precise contour. The system was validated using a representative set of 168 OCT-A images, providing accurate results with the best correlation with the manual measurements of two experts clinician of 0.93 as well as a Jaccard's index of 0.82 of the best experimental case. This tool provides an accurate FAZ measurement with the desired objectivity and reproducibility, being very useful for the analysis of relevant vascular diseases through the study of the retinal microcirculation.